Q39 / 125 · BITSAT 2016 · Chemistry

$\mathrm{Al}$ (at. wt 27 ) crystallizes in the cubic system with a cell edge of $4.05 Ã…$. Its density is $2.7 \mathrm{~g}$ per $\mathrm{cm}^{3}$. Determine the unit cell type calculate the radius of the $\mathrm{Al}$ atom

  • A
    $\mathrm{fcc}, 2.432 Ã$
  • B
    bcc, $2.432 Ã$
  • C
    bcc, $1.432 Ã$
  • Correct answer
    D
    $\mathrm{fcc}, 1.432 Ã$

Solution

$\rho=\frac{Z \times M}{N_{0} \times a^{3}}$, $$ 2.7=\frac{Z \times 27}{6.02 \times 10^{23} \times(4.05)^{3} \times 10^{-24}} $$ $\therefore Z=4$ Hence it is face centred cubic unit lattice. Again $4 r=a \sqrt{2}=5.727 Ã…$ $\therefore \mathrm{r}=1.432 Ã…$

Hence, the correct answer is option: 'D'.

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